Problem: If $\angle AOC$ is a right angle and $m \angle AOB = 80^\circ$, what is $m \angle BOC$, in degrees? $80^\circ$ $O$ $A$ $C$ $B$
From the diagram, we see that $\angle AOB$ and $\angle BOC$ are complementary angles. Therefore, $m \angle AOB + m \angle BOC = 90^\circ$ Thus, $m \angle BOC = 90^\circ - m \angle AOB = 90^\circ - 80^\circ = 10^\circ$.